Logarithm

1 is the natural logarithm of e.

The natural logarithm of e is 1.

The history of logarithm in seventeenth-century Europe is the discovery of a new function that extended the realm of analysis beyond the scope of algebraic methods.

In mathematics, the binary logarithm (log₂ n) is the power to which the number 2 must be raised to obtain the value n.

The binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2, and the binary logarithm of 32 is 5.

The binary logarithm also frequently appears in the analysis of algorithms, not only because of the frequent use of binary number arithmetic in algorithms, but also because binary logarithms occur in the analysis of algorithms based on two-way branching.

The natural logarithm base is sometimes also called Euler's number.

For a currency which uses denominations of 1, 2, 5, 10, 20, 50, 100, 200, 500, 1000, etc., each jump in the base-10 logarithm from one denomination to the next higher is either 0.3010 or 0.3979.